Session C01: Electronic Correlations in Topological Materials

Temperature Dependence of Charge Transport in an Undoped Weyl Semimetal – Y2Ir2O7

An undoped Weyl Semimetal (WSM) is predicted to exhibit resistivity varying with temperature as ρ α T^-4 in the presence of a random Coulomb potential screened by thermally generated charge carriers. Here we show that, in hydrothermally grown polycrystalline samples of the WSM Y₂Ir₂O₇, ρ = ρ₀T^-4 over four orders of magnitude in ρ. The prefactor, ρ₀, agrees with theoretical estimates within the random potential model using reasonable materials parameters. The model works well beyond its range of applicability, extending into the high-resistivity region where the Ioffe-Regel parameter, k_T l « 2π. The importance of strong electron correlations suggests this is behavior characteristic of a "bad-WSM".   

Higher-Order Symmetry Enriched Topological Phases

Higher-order topological insulators (TIs) exhibit boundary physics typically associated with lower dimensional TIs, e.g. 2-d second-order TIs exhibit localized 0-d zero energy corner modes. This physics is topologically protected as long as certain lattice symmetries are preserved, akin to topological crystalline insulators. So far, these phases have largely been explored in the context of non-interacting fermion systems. However, we know that symmetries may also "enrich" the physics of interacting topological phases, such as quantum spin liquids or fractional quantum Hall states. Is it possible to realize "higher-order" boundary physics in strongly interacting topological phases? In this talk, we discuss exactly such higher-order symmetry enriched topological phases, including an example of an exactly solvable spin model with a quantum spin liquid ground state that indeed exhibits topologically protected corner modes, a hallmark of second-order TIs.   

Topological Phases of the Interacting SSH and Kitaev Models on the Bethe Lattice

Topological phases of matter have been intensely studied in recent years, but there still remain a number of open questions regarding the interplay of topology and strong interactions in condensed matter systems, including the role of topological invariants. Two prototypical models in one dimension exhibiting non-trivial topological phases are the SSH model and the Kitaev chain. Here we study generalizations of these models on the Bethe lattice, showing that topological phases with bulk zero-modes can be realized in higher dimensions. We then consider interacting versions of these Bethe SSH and Kitaev models with local Hubbard interactions, U. These topological Hubbard models are solved exactly in infinite dimensions at T=0 using dynamical mean field theory with the numerical renormalization group as an impurity solver.

For the Bethe SSH Hubbard model with interactions U<U_c below a critical strength, bulk gapped sites at U=0 develop a power-law pseudogap density of states, while sites with topological zero-mode poles at U=0 are augmented by power-law diverging quasiparticle Kondo peaks. A bulk Mott insulating phase is realized for U>U_c. A method of characterizing the topological phases of the systems in the presence of interactions based on their Green's functions is discussed.   

Interacting multi-channel topological boundary modes in a quantum Hall valley system

Quantum Hall ferromagnets (QHFMs) are two-dimensional electronic phases with spontaneously broken spin or pseudospin symmetry whose wavefunctions also have topological properties. Domain walls between distinct broken symmetry QHFM phases are predicted to host gapless one-dimensional (1D) modes that emerge due to a topological change of the underlying electronic wavefunctions at such interfaces. Although a variety of QHFMs have been identified in different materials, probing interacting electronic modes at these domain walls has not yet been accomplished. Here we use a scanning tunneling microscope (STM) to directly visualize the spontaneous formation of boundary modes, within a sign-changing topological gap, at domain walls between different valley-polarized quantum Hall phases on the surface of bismuth. By changing the valley occupation and the corresponding number of modes at the domain wall, we can realize different regimes where the valley-polarized channels are either metallic or develop a spectroscopic gap. This behavior is a consequence of Coulomb interactions constrained by the symmetry-breaking valley flavor, which determines whether electrons in the topological modes can backscatter, making these channels a unique class of interacting Luttinger liquids.   

Interesting behavior of magnetoresistance in single crystals of CeBi

Cerium monopnictides, CeX (X= Sb, Bi) have gained renewed interest as potential candidates to host non-trivial topological band structure along with magnetism. High quality single crystals of CeBi were grown out of Bi self-flux. Systematic measurements of temperature and magnetic field dependent resistivity and magnetization were conducted on CeBi. A rich H-T phase diagram was mapped out. Interestingly, extremely large magnetoresistance was observed at low temperature, and large negative magnetoresistance was detected at the intermediate temperature regime. To obtain a better understanding of the system, the electronic structure is also being studied.   

Orbital Edelstein effect from spontaneous symmetry breaking

Coupling between charge and spin, and magnetoelectric effects more generally, have been an area of great interest for several years, with the sought-after ability to control magnetic degrees of freedom via electric currents serving as an impetus. The orbital Edelstein effect is a magnetoelectric effect consisting of a bulk orbital magnetization induced by an electric current. It is the orbital analogue of the spin Edelstein effect, in which the carriers’ spin gives rise to the magnetization. The orbital Edelstein effect has recently been investigated in the context of Weyl materials. Motivated by these developments, we examine a toy model in which a crystal exhibits such an orbital Edelstein effect upon symmetry breaking via density-wave order which reduces it to a gyrotropic crystal class.   

Observation of Double Weyl Phonons in Parity-Breaking FeSi

Condensed matter systems have now become a fertile ground to discover emerging topological quasiparticles with symmetry protected modes. While many studies have focused on fermionic excitations, the same conceptual framework can also be applied to bosons yielding new types of topological states. Motivated by Zhang et al.’s recent theoretical prediction of double Weyl phonons in transition metal monosilicides [Phys. Rev. Lett. 120, 016401 (2018)], we directly measure the phonon dispersion in parity-breaking FeSi using inelastic x-ray scattering. By comparing the experimental data with theoretical calculations, we make the first observation of double Weyl points in FeSi, which will be an ideal material to explore emerging bosonic excitations and its topologically nontrivial properties.
Physical Review Letters 121, 035302 (2018)   

Berryogenesis: self-induced Berry flux and spontaneous non-equilibrium magnetism

Spontaneous symmetry breaking is central to the description of interacting phases of matter. In this talk I will discuss a new mechanism through which a driven interacting system subject to a time-reversal symmetric driving field can spontaneously magnetize [1]. Strong internal ac fields of a metal driven close to its plasmon resonance may enable Berryogenesis: the spontaneous generation of a self-induced Bloch band Berry flux. The self-induced Berry flux supports and is sustained by a circulating plasmonic motion, which may arise even for a linearly polarized driving field. Berryogenesis relies on feedback due to interband coherences induced by internal fields, and may readily occur in a wide variety of multiband systems. We anticipate that graphene devices, in particular, provide a natural platform to achieve Berryogenesis and plasmon-mediated spontaneous non-equilibrium magnetization in present-day devices.

[1] Mark S. Rudner and Justin C. W. Song, arXiv:1807.01708 (2018).   

Higher angular momentum band inversions in two dimensions

This talk discusses a special class of topological phase transitions in two dimensions described by the inversion of bands with relative angular momentum higher than 1. A band inversion of this kind, which is protected by rotation symmetry, separates the trivial insulator from a Chern insulating phase with higher Chern number, and thus generalizes the quantum Hall transition described by a Dirac fermion. Higher angular momentum band inversions are of special interest, as the non-vanishing density of states at the transition can give rise to interesting many-body effects. We introduce a series of minimal lattice models which realize higher angular momentum band inversions. Interaction effects are considered, focusing on the possibility of electron-hole exciton condensation, which breaks rotational symmetry. We further describe how the notion of higher angular momentum band inversions can be generalized to time-reversal invariant systems. Such band inversions can be viewed as transitions to a topological insulator protected by rotation and inversion symmetry, and provide a promising venue for realizing correlated topological phases such as fractional topological insulators.   

Real-space recipes for interacting topological crystalline states

We present a unified scheme for constructing all topological crystalline states, bosonic and fermionic, free and interacting, from real-space building blocks and connectors. Building blocks are finite-size pieces of lower dimensional topological states protected by onsite symmetries alone, and connectors are ``glue'' that complete the open edges shared by two or multiple pieces of building blocks. The resulted assemblies are selected against two physical criteria we call the ``no-open-edge condition'' and the "bubble equivalence", which, respectively, ensure that each selected assembly is gapped in the bulk and cannot be deformed to a product state. The scheme is then applied to obtaining the full classification of bosonic topological crystalline states protected by several onsite symmetry groups and each of the 17 wallpaper groups in two dimensions and 230 space groups in three dimensions. We claim that our real-space recipes give the complete set of topological crystalline states for bosons and fermions, and prove the boson case analytically using a spectral sequence expansion of group cohomology.   

Non-Topological Majorana Zero Modes in Inhomogeneous Spin Ladders

We show that the coupling of homogeneous Heisenberg spin-1/2 ladders in different phases leads to the formation of interfacial zero energy Majorana bound states. Unlike Majorana bound states at the interfaces of topological quantum wires, these states are void of topological protection and generally susceptible to local perturbations of the host spin system. However, a key message of our work is that in practice they show a high degree of resilience over wide parameter ranges which may make them interesting candidates for applications.   

Symmetry-protected exceptional rings in two-dimensional correlated systems

Emergence of exceptional points in two-dimensional systems is one of the characteristic phenomena in non-Hermitian systems. In this talk, we elucidate the impacts of symmetry on the non-Hermitian degeneracies. In particular, we analyze correlated systems with chiral symmetry in equilibrium where the imaginary-part of the self-energy induces the non-Hermitian phenomenon. Intriguingly, our analysis discover novel topological degeneracies which we call symmetry-protected exceptional rings (SPERs). Furthermore, we demonstrate that SPERs emerge in a correlated honeycomb lattice by employing the dynamical mean-field theory combined with the numerical renormalization group.   

Large magneto-elastoresistance in WTe2

Elastoresistance is the relative change of a material’s resistance under strain. Its value depends on two contributions: one coming from changes in the sample’s geometry and another from changes of the electronic properties such as carrier densities or scatering rates. In common metals like copper, the geometric contribution dominates a temperature-independent elastoresistance with a value of about 2. In other materials, including Bi, changes in the electronic properties dominate. We find that WTe₂ is a member of the second group exhibiting an elastoresistance as large as -20. Moreover, we discover that the magnetic field has a dramatic effect on the elastoresistance in WTe₂, resulting in values of elastoresistance in applied magnetic field between -80 to 120. We present a detailed analysis of this phenomenon combining results from DFT calculations and quantum oscillation measurements. We conclude that such large magneto-elastoresistance can be realized in other semi-metals with crystal structures similar to WTe₂.   

Topological Order and Subsystem Symmetry

When a system is invariant under a subsystem symmetry, it is as if it has a "gauge" symmetry on particular subregions. Motivated by this obervation, we show that subsystem symmetries can lead to topological features remenescent of those found in topological gauge theories. This is done by considering a subsystem symmetry generalization of a Chern-Simons field theory. Because of the subsystem symmetry, this model has a robust ground state degeneracy on torus and localized zero energy corner modes.   

Topological properties of mirror symmetric Kondo half-metals

The concept of topology in condensed matter physics has been widely recognized since the theoretical discovery of topological insulators by Kane and Mele. Recently, the electron correlation effects on topological properties have attracted much attention because of nontrivial features that do not emerge in weakly correlated electron systems, such as topological Kondo insulators, magnetic orders in topological insulators, etc.
In the previous study, it has been elucidated that in the presence of spin U(1) symmetry, even ferromagnetic (FM) systems can acquire topological properties; system with spin U(1) symmetry can have a spin-selective gap which results in nontrivial topological properties. In general, however, spin U(1) symmetry is considered to be broken in heavy-fermion systems because of their strong spin-orbit coupling (SOC). This fact motivates us to ask whether the above topological phases can be realized in the presence of SOC.
In this study, we demonstrate that even in the absence of spin U(1) symmetry, ferromagnetic phases with mirror symmetry can have the topological properties. In particular, we analyze an effective model describing a thin film of SmB₆, and find the topological state in a half-metallic FM phase characterized by a mirror Chern number.